To find the Present Value (PV) and verify the Future Value (FV) of the investment, we use the Present Value formula and Future Value formula for each payment.

1. Present Value (PV) Calculation

The Present Value (PV) of an annuity is found using the discounting formula:

$PV = \sum \frac{C_t}{(1 + r)^t}$

Where:

• $C_t$ = Cash flow at year $t$
• $r = 7\% = 0.07$ (interest rate per year)
• $t$ = Year number

Applying the formula to each payment:

$PV = \frac{200}{(1.07)^1} + \frac{300}{(1.07)^2} + \frac{600}{(1.07)^3}$

Now, let's compute each term:

$PV = \frac{200}{1.07} + \frac{300}{(1.07)^2} + \frac{600}{(1.07)^3}$

$PV = 186.92 + 262.90 + 489.37$

$PV = 939.19$

2. Future Value (FV) Calculation

The Future Value (FV) of an investment is found using the compounding formula:

$FV = \sum C_t (1 + r)^{(n-t)}$

where:

• $n = 3$ (total number of years)

Applying the formula to each payment:

$FV = 200(1.07)^2 + 300(1.07)^1 + 600(1.07)^0$

$FV = 200(1.1449) + 300(1.07) + 600(1)$

$FV = 228.98 + 321 + 600$

$FV = 1149.98$

Thus,
Present Value (PV) = $939.19$
Future Value (FV) = $1149.98$ (confirmed)

Would you like a breakdown of any step?

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Related Questions

1. What happens to the PV if the interest rate increases to 10%?
2. How would the FV change if payments were made at the beginning of each year instead of the end?
3. If another $500 was added in Year 4, how would PV and FV be affected?
4. What is the total interest earned on this investment?
5. How does changing the compounding frequency (e.g., semi-annual) affect the FV?

Tip: The Present Value decreases as the interest rate increases, meaning higher discounting lowers the current worth of future payments.